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G. Kuiper: New developments and propeller design, 9th International Conference on Hydrodynamics, Shanghai, China, (2010).
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3 To simulate the rotational region around the propeller in FLUENT including the Coriolis acceleration in the RANS equations we have two options, MRF (moving reference frame method) and SLD (sliding mesh method). Although Mehdi et al. (2010).
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Standard K-epsilon Model.
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Realizable K-epsilon Model.
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Standard K-omega Model.
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Spalart Allmaras Model Second order upwind scheme has been used for momentum discretization and for the other equations. Simple scheme has been used to solve the pressure velocity coupling. The simulations are supposed to be converged when the residual is below 10-5. Propeller performance graphs and experimental results. The propeller performance curves have been calculated via three-dimensional Navier-Stokes flow solver FLUENT and compared with the experimental results. The Computed values of the propeller thrust and torque reached the measured values for each velocity but with different errors related to the used turbulence models as shows in Fig. 5. (a) (b) (c) (d) (e) (f) Fig. 5. P4119 simulation results for various turbulence modes with MRF: (a) Standard K-epsilon, (b) RNG K-epsilon, (c) Realizable K-epsilon, (d) standard K- omega, (e) SST K-omega, (f) Spalart Allmaras It should be pointed out that, the efficiency coefficient curves is not smooth for both the experimental and numerical results for all turbulence models after the advance coefficient J = 0. 9. This because the curves are created from small No. of points as the experimental data was only available for five advance coefficients as shown in Table 1. So, in-between the advance coefficients J = (0. 9 - 1. 1) there is no experimental data. On the other hand, the efficiency decreases sharply after J = 0. 9. Also related to the efficiency coefficient, there is a noticeable deviation between the experimental and numerical solution in-between the advance coefficient J = (0. 9 - 1. 1), and this deviation is not noticeable if the thrust and torque coefficients are considered. This high deviation may attribute to the definition of the efficiency coefficient it self as η=KTKQJ2π in addition to the computational errors. This deviation at advance coefficient J = (0. 9 - 1. 1) comes from three reasons, the first one is the computational error at J = 1. 1 is maximum. The second one is that, the term KTKQ in the definition of the efficiency represents the ratio between the smallest values for the thrust and torque, as the values for thrust coefficient and torque coefficient at J = 1. 1 are minimum. So the error of this ratio will be high when the individual terms are small. The third one is that, any error of the ratio between the thrust and the torque KTKQ will be multiplied with the value of the advance coefficient J. This means that for J < 1 the error will be decreased, on the other side the error will be increased for J > 1. Comparison between the results for used turbulence models. To further analyze the results, the error absolute (Δk) of the thrust coefficient, the torque coefficient and the efficiency coefficient have been calculated according to the following formula Δk=AbskExp. -knum. kExp. *100 and the error bar figures for thrust, torque and efficiency coefficients are as shown in Fig. 6-8. The comparison between results with different turbulence models shows that, at low advance coefficient the errors for all turbulence models are very small starting at J = 0. 5 with an error average ratio between the turbulence model equal to 1. 53 %, 1. 56 % and 4. 3% for KT, KQ and η. These errors start to slightly increase with the increasing of the advance coefficient till the error average ratio between the turbulence models at J = 0. 833 (operating advance coefficient) reaches 2. 9%, 3. 8% and 6. 4% for KT, KQ and η respectively. Then these errors start to highly increase till they reach the highest values with an error average ratio at J = 1. 1 reaches 38. 2%, 12% and 34. 5% for KT, KQ and η respectively. Fig. 6. Error bar for prediction of (KT) Fig. 7. Error bar for prediction of (KQ) Fig. 8. Error bar for prediction of (η) Table 2. Error percent ratio for RNG K-epsilon Model J RNG K-epsilon turbulence model KT KQ η.
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008 Table 3. Error percent ratio standard-K omega Model J standard-k omega turbulence model KT KQ η.
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690 Finally from the previous curves and the data analysis, RNG K-epsilon turbulence model appears to yield the best numerical solution of steady flow around marine propellers as shown in Fig. 5 (b) with an error ratio as shown in Table 2. And the standard-k omega model yields the highest error turbulence model as shown in Fig. 5 (d) and with an error ratio as shown Table 3. Conclusions This work shows that, the numerical simulation of marine propeller based on RANS equations is useful and suitable for understanding the flow around marine propeller but with some difficulties.
DOI: 10.1016/j.oceaneng.2012.01.012
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The accuracy of the CFD based on RANS equation is dependent on the used turbulence model. According to the steady flow simulation, the RNG K-epsilon turbulence model yields to provide the most accurate results, so it is recommended to do such this kind of simulation. On the other hand, the Standard K-omega model presents the highest error.
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All turbulence models have high accuracy at low advance coefficient even if Standard K-omega turbulence model which showed the highest error is considered. This accuracy is decreased with the increasing of advance coefficient with an acceptable range, but suddenly becomes very low at the high advance coefficient (J = 1. 1) even if RNG K-epsilon turbulence model which showed the lowest error is considered. This study of the steady simulation of the flow around marine propeller shows that, CFD is a powerful and reliable tool for calculating the propeller hydrodynamic characteristics. Even though it could not simulate the flow around the propeller at high advance coefficient with high accuracy, which is believed to be related to either the grid resolution or turbulence characteristics. Corresponding Author Name: Mohamed Bennaya E-mail: bennaya_m@yahoo. com Tel: 13674670715.
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